1. Field of the Invention
The invention relates generally to the field of well logging. More particularly, the invention relates to techniques for well logging using nuclear magnetic resonance tools and methods for inversion processing of nuclear magnetic resonance data.
2. Background Art
Oil well logging tools include nuclear magnetic resonance (NMR) instruments. NMR instruments can be used to determine properties of earth formations, such as the fractional volume of pore space, the fractional volume of mobile fluid filling the pore space, and the total porosity of earth formations. General background of NMR well logging is described in U.S. Pat. No. 6,140,817, assigned to the assignee hereof.
Signals measured by NMR logging tools typically arise from selected nuclei present in the probed volume. Because hydrogen nuclei are the most abundant and easily detectable, most NMR logging tools are tuned to detect hydrogen resonance signals (from either water or hydrocarbons). Hydrogen nuclei have different dynamic properties (e.g., diffusion rate and rotation rate) that are dependent on their environments (e.g., bound to pore surfaces versus free in fluids). The different dynamic properties of these nuclei manifest themselves in different nuclear spin relaxation times (i.e., spin-lattice relaxation time (T1) and spinxe2x80x94spin relaxation time (T2)). For example, hydrogen nuclei in viscous oils have relatively short relaxation times whereas hydrogen nuclei in light oils have relatively long relaxation times. Furthermore, the hydrogen nuclei in the free water (e.g., water in large vugs) typically have longer relaxation times than those in the bound water (e.g., clay-bound water). Consequently, these differing NMR relaxation times can provide information on properties of the earth formations.
Most NMR logging tools measure the spinxe2x80x94spin relaxation times (T2) to derive the properties of the earth formations. T2 relaxation is often measured from a train of spin-echoes that are generated with a series of pulses such as the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence or some variants of this. The CPMG pulse sequence is well known in the art. See Meiboom, S., Gill, D., 1958, xe2x80x9cModified Spin Echo Method for Measuring Nuclear Relaxation Times,xe2x80x9d Review of Scientific Instruments, 29, 688-91.
Once the NMR data are acquired, they are processed with any of a number of inversion methods known in the art to provide the desired information, for example, T2 distributions, from which the formation properties may be derived. The inversion of NMR data (e.g., the CPMG data) to provide accurate T2 distributions is a challenging problem because NMR measurements include information from fast and slow relaxing nuclei. Under well logging conditions, the long relaxing nuclei may not have sufficient time to fully relax (i.e., to be fully polarized by the static magnetic field). This necessitates polarization corrections before the NMR data are analyzed. On the other hand, the fast relaxing nuclei (e.g., those from clay-bound water) would have fully relaxed within a short wait time. Signals from these fast relaxing nuclei last only a few echoes and become undetectable afterwards. As a result, most of the collected spin echoes contain nothing but noise with respect to the fast relaxing nuclei, and accurate derivation of T2 distribution for the fast relaxing nuclei becomes difficult using conventional well logging and processing techniques.
Because fast T2 relaxation nuclei are generally associated with short T1 relaxation, the fast T2 relaxing nuclei can be better detected with rapidly repeated short wait time measurements (bursts). The high repetition rate of these burst measurements allows a better statistical averaging of signals from the fast T2 components. For example, U.S. Pat. No. 6,005,389 issued to Prammer (the Prammer patent) discloses a method of collecting NMR data with fast repeated pulse sequences that produce an improved signal to noise ratio (SNR) for the fast relaxing nuclei by stacking (averaging) of the measured data.
The T2 inversion of these bursts together with a standard CPMG measurement, however, poses some difficulty. If one were to combine these measurements in a common inversion process, one would need a good knowledge of the polarization correction for the burst measurements so that the residual contribution from partially polarized slow relaxing nuclei can be removed. xe2x80x9cA common inversionxe2x80x9d as used herein means a single inversion process using both measurements. Alternatively, a simplified assumption about the relation between polarization and T2 (or between T1 and T2) could be made so that a polarization correction term can be determined from two different wait time measurement sets. In an alternative approach, the burst measurements and the standard CPMG measurements may be separately inverted to produce independent T2 distributions, which are later combined to produce a common T2 distribution. See e.g., the Prammer patent. However, combining (or splicing) the two distributions into a common T2 distribution may result in less accurate inversion output.
Therefore, it is desirable to have methods that use common inversion on dual wait time measurements, but avoid problems associated with imperfect polarization corrections in the burst measurements.
One aspect of the invention relates to methods for inverting NMR measurements from well logging. According to embodiments of the invention, a method for determining an earth formation property from nuclear magnetic resonance measurements may include applying suppression functions to spin echoes in at least one burst measurement set to produce a modified burst data set, the suppression functions to suppress contribution of spin echoes having non-negligible polarization correction; inverting the modified burst data set and at least one standard spin echo measurement set to produce a nuclear magnetic resonance parameter distribution, the at least one standard spin echo measurement set and the at least one burst measurement set being acquired on an earth formation sample; and computing the earth formation property from the nuclear magnetic resonance parameter distribution. The nuclear magnetic resonance parameter includes at least one selected from longitudinal relaxation time, transverse relaxation time, a ratio of longitudinal relaxation time to transverse relaxation time, and diffusion constant. The suppression functions may comprise linear combination functions. The linear combination functions may comprise a null space of a matrix describing exponential decays of nuclear magnetizations according to acquisition parameters. The null space may be determined by singular value decomposition.
Another aspect of the invention relates to methods for determining a property of earth formations surrounding a wellbore using NMR instruments. In some embodiments of the invention, a method for determining a property of earth formations surrounding a wellbore may include inducing a static magnetic field in an area of investigation in the earth formations; acquiring at least one standard spin echo measurement set and at least one burst measurement set by applying spin echo pulse sequences comprising radio frequency magnetic field pulses in the area of investigation and receiving spin echo signal magnitudes; applying suppression functions to spin echoes in at least one burst measurement set to produce a modified burst data set, the suppression functions to suppress contribution of spin echoes having non-negligible polarization correction; and computing the property of the earth formations from the at least one standard spin echo measurement set and the modified burst data set.
Other aspects and advantages of the invention will be apparent from the following description and the appended claims.